Asymptotic Conditional Probability in Modal Logic: A Probabilistic Reconstruction of Nonmonotonic Logic
Abstract
We analyze the asymptotic conditional validity of modal formulas, i.e., the probability that a formula ψ is valid in the finite Kripke structures in which a given modal formula ϕ is valid, when the size of these Kripke structures grows to infinity. We characterize the formulas ψ that are almost surely valid (i.e., with probability 1) in case ϕ is a flat, S5consistent formula, and show that these formulas ψ are exactly those which follow from ϕ according to the nonmonotonic modal logic S5G. Our results provide – for the first time – a probabilistic semantics to a well-known nonmonotonic modal logic, establishing a new bridge between nonmonotonic and probabilistic reasoning, and give a computational account of the asymptotic conditional validity problem in Kripke structures.
Cite
Text
Rosati and Gottlob. "Asymptotic Conditional Probability in Modal Logic: A Probabilistic Reconstruction of Nonmonotonic Logic." International Joint Conference on Artificial Intelligence, 2005. doi:10.3760/cma.j.cn115330-20231031-00180Markdown
[Rosati and Gottlob. "Asymptotic Conditional Probability in Modal Logic: A Probabilistic Reconstruction of Nonmonotonic Logic." International Joint Conference on Artificial Intelligence, 2005.](https://mlanthology.org/ijcai/2005/rosati2005ijcai-asymptotic/) doi:10.3760/cma.j.cn115330-20231031-00180BibTeX
@inproceedings{rosati2005ijcai-asymptotic,
title = {{Asymptotic Conditional Probability in Modal Logic: A Probabilistic Reconstruction of Nonmonotonic Logic}},
author = {Rosati, Riccardo and Gottlob, Georg},
booktitle = {International Joint Conference on Artificial Intelligence},
year = {2005},
pages = {1378-1383},
doi = {10.3760/cma.j.cn115330-20231031-00180},
url = {https://mlanthology.org/ijcai/2005/rosati2005ijcai-asymptotic/}
}